What invasion led to great Britain entering world war 1?

Germany invaded Belgium as a path to get to France. (France and Germany had already mutually declared war in support of Austria-Hungary vs. Russia.) The French army was waiting for them on the Frech-German border but by passing thru neutral Belgium, Germany was able to get their army BEHIND the French army. It was called Schlieffen Plan after the German Field Marshal Alfred Graf von Schlieffen, who developed it. Britain had decades earlier pledged to guarantee the territorial integrity of Belgium as it had previously been coveted by Germany, France, and The Netherlands. Actually, it had previously been PART of The Netherlands and its independence was when Britain pledged its support. Germany gambled that Britain would NOT honor its commitment to go to war in support of Belgium. It was STUPID of Germany to think that Britain would ignore its responsibility.